**Q-Stem(Rephrased)**

We are asked is 1/2 *CB * AC = 1/2 * AD * AB or IS CB X AC = AD X AB ?

**St(1) :- AC X AC = 2 (AD X AD)**

It doesn't tell us anything about CB and AB that are necessary to answer the question stem.

**Insufficient****St (2) :- ABC is isosceles**

Let the side AC =x units => BC =x units too and ABC is a 45-45-90 triangle.

AB = sqrt(2)x but we have no information about AD.

**(Insufficient)****Combining both,**

AC=BC=x units and AB = sqrt(2) x

=>

**Area of ABC = 1/2 * x*x****= x^2/2**

From St(1), AD = Sqrt(AC^2/2) = Sqrt (x^2/2)

ABC area = 1/2 *x*x =x^2/2

ABD area = 1/2 * AB * AD

= 1/2 * √2 x * √(x^2)/2

= ½ * √2 x * x/√2

= x^2/2

Thus area of ABC =area ABD

**(Sufficient)****(option c)**